Hi sana.noor,

For this DS question, you can probably get through the first couple of steps fairly quickly, but you'll need a drawing to get through the final step.

We're told that there are 3 points: A, B and C. We're asked if the slope of line BC is negative. This is a YES/NO question.

Fact 1 tells us that line AB has a -1 slope. This doesn't tell us anything about where point C is relative to the other points.
So, the slope of BC could be positive and the answer is NO.
The slope of BC could be negative and the answer is YES.
Inconsistent = INSUFFICIENT

Fact 2 tells us that angle ABC is 37 degrees. We still don't know the slopes of anything.
Inconsistent = INSUFFICIENT

Combining steps, you'll want to draw a picture...

Line AB has a slope of -1. Draw THAT LINE. With a -1 slope, you'll be going down-and-to-the-right at a 45 degree angle.
Line BC has to come off of that first line at a 37 degree angle. If you draw all the possibilities, you'll see that line BC will ALWAYS be negative.
Consistent YES answer = SUFFICIENT

GMAT assassins aren't born, they're made,
Rich

sana.noor wrote:In the xy-plane, points A, B and C are not on the same line. Is the slope of line BC negative?

1. The slope of line AB is -1.
2. The measure of angle ABC is 37 degrees.

Target question: Is the slope of line BC negative?


Rich has aptly shown why statements 1 and 2 (alone) are NOT SUFFICIENT.
As he suggests, it's useful to draw the line with slope -1 and see what happens.
So, I thought I'd add the lines here.
This takes us to . . .

Statements 1 and 2 combined
If we draw the line segment AB with slope -1, then we get something like this:


If we add some lines parallel to the x- and y-axes, we need to recognize that we get 45-degree angles at point B


So, if we add a 37-degree angle at point B, we get one of two possible scenarios

or


In both cases, the slope of line BC is definitely negative.
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent